RatLand is a large family theme park located in central Texas. Over the years a visit to Ratland has been institutionalized as a prime “have to” experience for children growing up in America. Additionally, Ratland has developed a significant international following among Asians and the British, making it one of the prime international vacation destinations of any location on the globe. The Ratland experience is based on the various exploits of a group of loosely associated animal cartoon characters led by Roué the Rat and originally developed early in the Great Depression. The Roué the Rat franchise had become less popular as the years passed until brilliant marketing of the Ratland concept gave the characters new life in the 1960s. Now adults with fond memories of visiting Ratland as children bring their own children.

Ratland is planning for a new attraction scheduled to open in the Spring of 2020. (The opening will correspond with the 90th anniversary of the release of the first Roué the Rat cartoon.) “Rambo Squirrel’s Wild Water Massacre Splash” will be a theater-based experience in which patrons will be brought into a 420-seat theater for a precisely timed 15-minute experience that never varies in length. The presentation will be a combination of video and laser-generated special effects. The height of the show will feature Rambo Squirrel mowing down his woodland friends all in fun with a semi-automatic super-soaker machine gun connected to a garden hose. (Rambo Squirrel Hose Guns will be available for purchase in an attached gift shop for more fun at home.)

In an average hour 1700 Ratland patrons are expected to approach and join the line for the Rambo Squirrel attraction on a busy summer day. They will be brought into the theater in groups no larger than 500 to experience the 15-minute show, then are quickly ushered out of the theater and a new group is brought in. Emptying and refilling the theater will be very well coordinated and expected to take five minutes. The Rambo Squirrel Design Team understands the dynamics of queues.

a. On a busy summer day how long on average will be the line of patrons waiting to enter the Rambo Squirrel attraction?

b. A soft drink maker is considering sponsoring the attraction at Ratland. However, in exchange for a sponsorship fee the sponsor want the presentation’s script written such that their product is mentioned by the Ratland characters 3 times during the presentation and Rambo Squirrel is shown drinking the product before hosing down his friends. All this will add 20 seconds to the entire performance. If this is done how much (if any) will patron wait time be impacted by this product placement?

c. By how much would the theater capacity need to be increased to eliminate the extra wait time originating from the sponsor’s product placement?